Question

the value of $\tan {20}^{\circ }+2\tan {50}^{\circ }-\tan {70}^{\circ }$ is :

• A. 1
• B. 0
• C. $\tan {50}^{\circ }$
• D. none of these

Answer 1

The correct option is B 0

$a=\tan 20+2\tan 50-\tan 70=\tan 20+\tan 50+\tan 50-\tan 70$
$\Rightarrow a=\frac{\sin 20\cos 50+\cos 20\sin 50}{\cos 20\cos 50}+\frac{\sin 50\cos 70-\cos 50\sin 70}{\cos 70\cos 50}$
$\Rightarrow a=\frac{\sin (20+50)}{\cos (90-70)\cos 50}+\frac{\sin (50-70)}{\cos (90-20)\cos 50}$ $\{\because \sin A\cos B+\cos A\sin B=\sin (A+B)\&\sin A\cos B-\cos A\sin B=\sin (A-B)\}$
$\Rightarrow a=\frac{\sin 70}{\sin 70\cos 50}-\frac{\sin 20}{\sin 20\cos 50}=0$
Ans: B